Learn CAT Quantitative Aptitude: Problems based on Averages

Problem 1:

If in a certain shipment of new cars, the cost of car X is twice the average of the other 11     cars in the shipment, what fraction of the total cost of 12 cars is the cost of car X?

Solution:

Let the cost of the other 11 cars combined be T.

So the average cost of each of these 11 cars is   . Hence the cost of car X  is  .

Now, the fraction that we want to find is 

This is equal to    divided by 

Therefore, choice [3] is the answer.

Problem 2:

At the Scholarly Text Printing Company, each of n printing presses can produce on the average t books every m minutes. If all presses work without interruption, how many hours will be required to produce a run of 10,000 books?

Solution:

This question asks us to express a certain relationship in an algebraic notation relating average to total number.

Each machine operates at the rate of t books per m minutes or 

But there are n such machines, so the overall rate of operation will be n times    which is .

To find the time it will take to produce 10,000 books, we divide that number by the rate of operation:

Therefore, 

Finally, we divide the above by 60 since there are 60 minutes in every hour to get the answer as  Therefore the correct option is [3].

Problem 3:
A sequence of seven consecutive integers is given. The average of the first five integers is n. The average of all the seven integers is:

[1] n

[2] n + 1

[3] n + 2

[4] kn, where k is a function of n

Solution:
This problem appeared in CAT 2000…but it is rather an easy one!

Let the consecutive integers be:(a+1),(a+2),(a+3),(a+4),(a+5)

Then, the average of first five integers can be given as:

Similarly, the average of first seven integers can be given as:

7a+28=X (where X is the number we need to find)

Now, from (i) we can say that 7a+21=7n (i.e., multiplying (i) by 7)

therefore (7a+21)+7=X

7n+7=X or  =(n+1) [i.e. the sum of the first seven integers equals(n+1),

                                 therefore option 2 is the correct option.]

Note: A much quicker way to solve the problem could have been to assume 1, 2, 3, 4, 5 as the consecutive integers and then proceeding to get the answer. Try it yourself!